Exploring Quadratic Transformations

What is the equation for the quadratic parent function?

• f(x) = 2x

• f(x) = x^2

• f(x) = x

• f(x) = x^3

What effect does a value of 'a' greater than 1 have on a parabola?

• Horizontal compression

• Horizontal stretch

• Vertical compression

• Vertical stretch

What does a value of 'b' less than 1 but greater than 0 cause?

• Vertical stretch

• Horizontal compression

• Horizontal stretch

• Vertical compression

How does a value of 'a' between 0 and 1 affect the parabola?

• Shifts it to the right

• Shifts it to the left

• Makes it wider

• Makes it narrower

What does a negative value outside the function cause?

• Shift to the left

• Shift to the right

• Reflection across the x-axis

• Reflection across the y-axis

What does adding a value inside the function cause?

• Vertical shift

• Horizontal shift

• Horizontal stretch

• Vertical stretch

What is the result of a negative value inside the function?

• Vertical shift upwards

• Horizontal shift to the right

• Reflection across the y-axis

• Reflection across the x-axis

What does the equation 'G(x) = -f(x)' imply about the graph?

• It shifts to the left

• It becomes narrower

• It reflects across the x-axis

• It reflects across the y-axis

What effect does 'G(x) = 2f(x)' have on the parabola?

• Horizontal compression

• Vertical stretch

• Horizontal stretch

• Vertical compression

What does 'G(x) = (x + 3)^2' indicate about the graph's transformation?

• Shifts 3 units to the left

• Becomes wider

• Becomes narrower

• Shifts 3 units to the right